5. In an Argand diagram, the points \(A\) and \(B\) are represented by the complex numbers \(- 3 + 2 \mathrm { i }\) and \(5 - 4 \mathrm { i }\) respectively. The points \(A\) and \(B\) are the end points of a diameter of a circle \(C\).
- Find the equation of \(C\), giving your answer in the form
$$| z - a | = b \quad a \in \mathbb { C } , b \in \mathbb { R }$$
The circle \(D\), with equation \(| z - 2 - 3 \mathrm { i } | = 2\), intersects \(C\) at the points representing the complex numbers \(z _ { 1 }\) and \(z _ { 2 }\)
- Find the complex numbers \(z _ { 1 }\) and \(z _ { 2 }\)
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